Chapter 6, Problem 23CR

To determine

The solution of the percent problem “ $48$ is what percent of $32$ ?” with equation.

Answer to Problem 23CR

  $150\%$

Explanation of Solution

Given:

The percent problem “ $48$ is what percent of $32$ ?”.

Concept used:

To translate a phrase of the form “ $A$ is what percent of $B$ ?” to an equation. First, assume that the percent is x . Then, read the statement “ $A$ is $x\%$ of $B$ ”. In “ $x\%$ of $B$ ” the word “of” represents “multiplication”. So, the given statement can be translated in to an equation as follows:

  $\begin{array}{ccccc}\text{A}& \text{is}& \text{what percent}& \text{of}& B\\ \downarrow & \downarrow & \downarrow & \downarrow & \downarrow \\ A& =& x& ·& B\end{array}$

So, the equation becomes $A=x·B$ .

Calculation:

Using the concept, the given statement can be translated into an equation as

  $48=x\cdot 32$ .

Now, solve the equation as follows:

  $\begin{array}{c}\text{ 48}=x\cdot 32\\ \frac{48}{32}=\frac{x\cdot 32}{32}\text{Divide both sides with 32}\text{.}\\ \frac{48}{32}=x\\ 1.5=x\\ x=1.5\end{array}$

Next, since we are looking for percent, we can write $1.5$ as a percent.

  $x=150\%$

Conclusion:

The solution of the percent problem is $150\%$ .